KiDS-1000: Cross-correlation with <i>Planck</i> cosmic microwave background lensing and intrinsic alignment removal with self-calibration

Galaxy shear - cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology to auto-correlations. While being immune certain systematic effects, they are affected by the galaxy intrinsic alignments (IA). This may be responsible for reported low amplitude of $\times$ CMB cross-correlations, compared standard Planck $\Lambda$CDM (cosmological constant and cold dark matter) prediction. In this work, we investigate how IA affects Kilo-Degree Survey (KiDS) cross-correlation compare it previous treatments with or without taken into consideration. More specifically, marginalization over parameters self-calibration (SC) method (with observables defined only from source galaxies) prove that SC can efficiently break degeneracy between $A_{\rm lens}$ IA}$. We further different systematics affect resulting IA}$ lens}$, validate our results MICE2 simulation. find including constrain IA, loss due is strongly reduced. The best-fit values lens}=0.84^{+0.22}_{-0.22}$ IA}=0.60^{+1.03}_{-1.03}$, while angular scale cuts $\sim10\%$. show appropriate treatment boost factor, magnification, photometric redshift modeling important obtaining correct cosmological results.